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SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 374850hv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374850.hv2 | 374850hv1 | \([1, -1, 0, 24282333, 331737662241]\) | \(1181569139409959/36161310937500\) | \(-48459615146628881835937500\) | \([2]\) | \(141557760\) | \(3.6086\) | \(\Gamma_0(N)\)-optimal |
| 374850.hv1 | 374850hv2 | \([1, -1, 0, -595873917, 5338259068491]\) | \(17460273607244690041/918397653311250\) | \(1230740691562636221269531250\) | \([2]\) | \(283115520\) | \(3.9552\) |
Rank
sage: E.rank()
The elliptic curves in class 374850hv have rank \(1\).
Complex multiplication
The elliptic curves in class 374850hv do not have complex multiplication.Modular form 374850.2.a.hv
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
